Data description

setwd("~/Documents/LSHTMproject/Rcode")

load("LCA.Rdata")

library(epiDisplay)
library(plyr)
library(tidyverse)
library(poLCA)
# Number of subjects per survey year
with(NDNS, tab1(SurveyYear, graph = FALSE, decimal = 2))
## SurveyYear : 
##             Frequency Percent Cum. percent
## NDNS Year 1       801   13.01        13.01
## NDNS Year 2       812   13.19        26.21
## NDNS Year 3       782   12.71        38.91
## NDNS Year 4      1055   17.14        56.05
## NDNS Year 5       625   10.15        66.21
## NDNS Year 6       663   10.77        76.98
## NDNS Year 7       703   11.42        88.40
## NDNS Year 8       714   11.60       100.00
##   Total          6155  100.00       100.00
# Number of subjects per servey year by gender where Men == 1, Women == 2

with(NDNS, tabpct(SurveyYear, Sex,  graph = FALSE, decimal = 2))
## 
## Original table 
##              Sex
## SurveyYear        1     2  Total
##   NDNS Year 1   336   465    801
##   NDNS Year 2   350   462    812
##   NDNS Year 3   339   443    782
##   NDNS Year 4   418   637   1055
##   NDNS Year 5   249   376    625
##   NDNS Year 6   254   409    663
##   NDNS Year 7   321   382    703
##   NDNS Year 8   270   444    714
##   Total        2537  3618   6155
## 
## Row percent 
##              Sex
## SurveyYear          1       2  Total
##   NDNS Year 1     336     465    801
##                (41.9)  (58.1)  (100)
##   NDNS Year 2     350     462    812
##                (43.1)  (56.9)  (100)
##   NDNS Year 3     339     443    782
##                (43.4)  (56.6)  (100)
##   NDNS Year 4     418     637   1055
##                (39.6)  (60.4)  (100)
##   NDNS Year 5     249     376    625
##                (39.8)  (60.2)  (100)
##   NDNS Year 6     254     409    663
##                (38.3)  (61.7)  (100)
##   NDNS Year 7     321     382    703
##                (45.7)  (54.3)  (100)
##   NDNS Year 8     270     444    714
##                (37.8)  (62.2)  (100)
## 
## Column percent 
##              Sex
## SurveyYear        1        %     2        %
##   NDNS Year 1   336  (13.24)   465  (12.85)
##   NDNS Year 2   350  (13.80)   462  (12.77)
##   NDNS Year 3   339  (13.36)   443  (12.24)
##   NDNS Year 4   418  (16.48)   637  (17.61)
##   NDNS Year 5   249   (9.81)   376  (10.39)
##   NDNS Year 6   254  (10.01)   409  (11.30)
##   NDNS Year 7   321  (12.65)   382  (10.56)
##   NDNS Year 8   270  (10.64)   444  (12.27)
##   Total        2537    (100)  3618    (100)
# summary of their age 

NDNS %>% 
  group_by(SurveyYear, Sex) %>% 
  summarise(N = n(), MeanAge = mean(Age), SDAge = sd(Age), minAge = min(Age), maxAge = max(Age))
## # A tibble: 16 x 7
## # Groups:   SurveyYear [?]
##    SurveyYear  Sex       N MeanAge SDAge minAge maxAge
##    <chr>       <chr> <int>   <dbl> <dbl>  <dbl>  <dbl>
##  1 NDNS Year 1 1       336    49.9  17.3     19     86
##  2 NDNS Year 1 2       465    49.2  17.8     19     94
##  3 NDNS Year 2 1       350    48.9  17.3     19     96
##  4 NDNS Year 2 2       462    50.2  17.9     19     92
##  5 NDNS Year 3 1       339    48.5  16.9     19     87
##  6 NDNS Year 3 2       443    49.6  18.0     19     93
##  7 NDNS Year 4 1       418    51.4  17.0     19     90
##  8 NDNS Year 4 2       637    48.8  17.0     19     94
##  9 NDNS Year 5 1       249    51.7  16.6     19     93
## 10 NDNS Year 5 2       376    49.4  17.8     19     92
## 11 NDNS Year 6 1       254    51.1  17.7     19     93
## 12 NDNS Year 6 2       409    49.0  18.1     19     95
## 13 NDNS Year 7 1       321    51.5  18.3     19     92
## 14 NDNS Year 7 2       382    49.8  18.3     19     89
## 15 NDNS Year 8 1       270    50.4  16.8     19     90
## 16 NDNS Year 8 2       444    49.9  17.7     19     94
# Dietary data by day

vecid1<-unique(dta_day1$id) # n = 6153
vecid2<-unique(dta_day2$id) # n = 6153
vecid3<-unique(dta_day3$id) # n = 6151
vecid4<-unique(dta_day4$id) # n = 6026

setdiff(vecid, vecid1) # two subjects did not have day 1 data
## [1] 50506161 70908241
setdiff(vecid, vecid2) # two subjects did not have day 2 data
## [1] 31012251 40714261
setdiff(vecid, vecid3) # four subjects did not have day 3 data
## [1] 10914251 11205071 80702191 81210131
setdiff(vecid, vecid4) # 129 subjects did not have day 4 data
##   [1] 10112011 10701161 10702161 10707261 10906181 10910111 10914251
##   [8] 20106041 20116171 20202081 20205081 20301211 20307041 20405101
##  [15] 20509211 20602011 20615041 21002101 21011041 21107031 21113041
##  [22] 21211041 21211101 30113231 30205131 30205201 30402131 30404081
##  [29] 30411081 30417081 30603071 30605131 30609131 30708201 30709031
##  [36] 30906071 30906201 30907251 30912021 31110201 40101011 40104021
##  [43] 40109221 40116011 40214081 40221221 40315101 40402221 40410251
##  [50] 40504211 40506221 40516021 40710081 40710101 40714251 40714261
##  [57] 40803081 40803221 40808081 40814131 40816011 40902051 40904021
##  [64] 41012081 41016131 41202051 50104191 50105161 50306241 50310271
##  [71] 50501271 50504271 50710161 51002141 51002191 51004011 51102241
##  [78] 51203191 51205141 51208041 51209071 60202081 60202261 60206161
##  [85] 60310131 60313021 60405161 60508071 60606271 60808161 60909271
##  [92] 61013261 61102251 61109081 70113191 70302241 70305031 70309241
##  [99] 70311181 70311251 70407251 70613181 70703181 70714181 70802241
## [106] 70812251 70815241 71101061 71206191 80108061 80301061 80301281
## [113] 80302191 80308251 80312241 80405181 80405281 80410131 80611131
## [120] 80713281 80805191 81002251 81004251 81005191 81007061 81101221
## [127] 81110061 81110131 81203221

day 1 data (3 classes)

# LCA in day1 -------------------------------------------------------------

# noquote(paste(rep("H", 24), 0:23, sep = ""))
#H0  H1  H2  H3  H4  H5  H6  H7  H8  H9  H10 H11 H12 H13 H14 H15 H16 H17 H18 H19 H20 H21 H22 H23

f <- cbind(H0, H1, H2, H3, H4, H5, H6, H7, H8, H9, H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22,H23) ~ 1
lc3 <- poLCA(f, dta_d1_wide, nclass = 3, graphs = TRUE, maxiter = 10000)

## Conditional item response (column) probabilities,
##  by outcome variable, for each class (row) 
##  
## $H0
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0008   0.0088    0.0052     0.9853
## class 2:    0.0003   0.0103    0.0067     0.9827
## class 3:    0.0429   0.0566    0.0028     0.8978
## 
## $H1
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0075    0.0021     0.9904
## class 2:    0.0000   0.0026    0.0045     0.9929
## class 3:    0.0142   0.0210    0.0043     0.9605
## 
## $H2
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0040    0.0028     0.9932
## class 2:    0.0000   0.0015    0.0026     0.9959
## class 3:    0.0103   0.0065    0.0017     0.9814
## 
## $H3
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0035    0.0045     0.9920
## class 2:    0.0000   0.0005    0.0028     0.9967
## class 3:    0.0078   0.0064    0.0000     0.9858
## 
## $H4
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0004   0.0080    0.0043     0.9873
## class 2:    0.0000   0.0033    0.0024     0.9942
## class 3:    0.0088   0.0062    0.0021     0.9828
## 
## $H5
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0001   0.0144    0.0082     0.9772
## class 2:    0.0011   0.0080    0.0047     0.9862
## class 3:    0.0063   0.0076    0.0050     0.9810
## 
## $H6
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0125   0.0896    0.0496     0.8483
## class 2:    0.0131   0.0718    0.0312     0.8839
## class 3:    0.0377   0.1171    0.0279     0.8173
## 
## $H7
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0078   0.1996    0.1135     0.6790
## class 2:    0.0168   0.2212    0.1131     0.6488
## class 3:    0.0334   0.1689    0.0572     0.7405
## 
## $H8
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0214   0.2383    0.1254     0.6149
## class 2:    0.0205   0.2472    0.1447     0.5876
## class 3:    0.0599   0.2562    0.0775     0.6063
## 
## $H9
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0093   0.2087    0.0985     0.6835
## class 2:    0.0096   0.2228    0.1097     0.6579
## class 3:    0.0546   0.2483    0.0832     0.6139
## 
## $H10
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0125   0.2298    0.1152     0.6425
## class 2:    0.0139   0.2616    0.1228     0.6017
## class 3:    0.0610   0.2755    0.0643     0.5992
## 
## $H11
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0130   0.1524    0.0842     0.7504
## class 2:    0.0108   0.2041    0.0968     0.6882
## class 3:    0.0655   0.2294    0.0731     0.6320
## 
## $H12
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0542   0.5103    0.0924     0.3431
## class 2:    0.0094   0.1012    0.0440     0.8454
## class 3:    0.0599   0.2691    0.0712     0.5998
## 
## $H13
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0021   0.0264    0.0539     0.9176
## class 2:    0.0764   0.8092    0.1144     0.0000
## class 3:    0.0920   0.2995    0.0408     0.5677
## 
## $H14
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0153   0.2544    0.0717     0.6587
## class 2:    0.0010   0.0799    0.0556     0.8635
## class 3:    0.0872   0.2539    0.0692     0.5897
## 
## $H15
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0172   0.2245    0.1004     0.6579
## class 2:    0.0133   0.2127    0.1096     0.6643
## class 3:    0.1038   0.1829    0.0639     0.6493
## 
## $H16
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0195   0.2016    0.0718     0.7071
## class 2:    0.0212   0.2017    0.0961     0.6810
## class 3:    0.0992   0.2214    0.0690     0.6104
## 
## $H17
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0416   0.2539    0.0509     0.6537
## class 2:    0.0324   0.2211    0.0546     0.6918
## class 3:    0.0888   0.2344    0.0412     0.6356
## 
## $H18
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0407   0.3341    0.0516     0.5736
## class 2:    0.0642   0.3476    0.0469     0.5413
## class 3:    0.1420   0.1863    0.0318     0.6400
## 
## $H19
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0418   0.2486    0.0607     0.6489
## class 2:    0.0637   0.2761    0.0555     0.6047
## class 3:    0.1974   0.2652    0.0115     0.5259
## 
## $H20
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0320   0.2446    0.0771     0.6463
## class 2:    0.0497   0.2495    0.0701     0.6307
## class 3:    0.2720   0.2362    0.0247     0.4670
## 
## $H21
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0330   0.2388    0.0819     0.6464
## class 2:    0.0444   0.2366    0.0940     0.6250
## class 3:    0.2768   0.1542    0.0135     0.5555
## 
## $H22
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0168   0.1411    0.0552     0.7869
## class 2:    0.0260   0.1551    0.0620     0.7569
## class 3:    0.2027   0.1783    0.0319     0.5871
## 
## $H23
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0021   0.0408    0.0204     0.9366
## class 2:    0.0070   0.0432    0.0210     0.9288
## class 3:    0.0854   0.0974    0.0112     0.8061
## 
## Estimated class population shares 
##  0.4571 0.4171 0.1258 
##  
## Predicted class memberships (by modal posterior prob.) 
##  0.4635 0.4492 0.0873 
##  
## ========================================================= 
## Fit for 3 latent classes: 
## ========================================================= 
## number of observations: 6153 
## number of estimated parameters: 218 
## residual degrees of freedom: 5935 
## maximum log-likelihood: -99389.52 
##  
## AIC(3): 199215
## BIC(3): 200681
## G^2(3): 92059.43 (Likelihood ratio/deviance statistic) 
## X^2(3): 2.789386e+19 (Chi-square goodness of fit) 
## 
# lc3$llik #log-likelihood of model
# 
# lc3$P #Estimated class population shares 
# 
# lc3$predclass

day 1 data (Fig.)

Model comparison and selection

Model Comparison. (Day 1, n = 6153)
N of classes N of parameters G^2 df AIC BIC log-likelihood
1 72 94737.22 6081 201600.8 202085.0 -100728.40
2 145 93030.90 6008 200040.5 201015.6 -99875.26
3 218 92059.43 5935 199215.0 200681.0 -99389.52
4 291 91790.97 5862 199092.6 201049.5 -99255.29
5 364 90721.07 5789 198168.7 200616.5 -98720.35
6 437 90716.77 5716 198310.4 201249.1 -98718.20
7 510 89850.47 5643 197590.1 201019.7 -98285.04
Note:
Abbreviation: N, number; G^2, the likelihood ratio statistic; df, degree of freedom; AIC, Akaike information criterion; BIC, Bayesian information criterion.

Five classes visualisation

## Conditional item response (column) probabilities,
##  by outcome variable, for each class (row) 
##  
## $H0
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0021   0.0054    0.0000     0.9925
## class 2:    0.0000   0.0100    0.0070     0.9830
## class 3:    0.0532   0.0733    0.0040     0.8695
## class 4:    0.0036   0.0091    0.0028     0.9845
## class 5:    0.0007   0.0128    0.0095     0.9771
## 
## $H1
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0022    0.0025     0.9954
## class 2:    0.0002   0.0025    0.0048     0.9925
## class 3:    0.0197   0.0327    0.0065     0.9411
## class 4:    0.0000   0.0002    0.0024     0.9974
## class 5:    0.0000   0.0116    0.0022     0.9862
## 
## $H2
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0000    0.0063     0.9937
## class 2:    0.0000   0.0012    0.0020     0.9968
## class 3:    0.0148   0.0126    0.0014     0.9711
## class 4:    0.0000   0.0013    0.0013     0.9974
## class 5:    0.0000   0.0056    0.0025     0.9919
## 
## $H3
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0000    0.0051     0.9949
## class 2:    0.0000   0.0006    0.0025     0.9969
## class 3:    0.0111   0.0123    0.0000     0.9766
## class 4:    0.0000   0.0000    0.0019     0.9981
## class 5:    0.0000   0.0049    0.0050     0.9901
## 
## $H4
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0070    0.0037     0.9892
## class 2:    0.0000   0.0031    0.0016     0.9954
## class 3:    0.0112   0.0063    0.0035     0.9789
## class 4:    0.0017   0.0062    0.0011     0.9910
## class 5:    0.0000   0.0078    0.0062     0.9860
## 
## $H5
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0191    0.0067     0.9742
## class 2:    0.0009   0.0057    0.0034     0.9900
## class 3:    0.0074   0.0089    0.0000     0.9837
## class 4:    0.0020   0.0133    0.0105     0.9742
## class 5:    0.0000   0.0109    0.0085     0.9807
## 
## $H6
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0165   0.1007    0.0441     0.8387
## class 2:    0.0117   0.0706    0.0290     0.8887
## class 3:    0.0380   0.1185    0.0293     0.8141
## class 4:    0.0189   0.0964    0.0433     0.8414
## class 5:    0.0111   0.0755    0.0477     0.8657
## 
## $H7
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0082   0.2176    0.0971     0.6772
## class 2:    0.0204   0.2084    0.1070     0.6642
## class 3:    0.0447   0.1450    0.0521     0.7582
## class 4:    0.0038   0.2386    0.1334     0.6241
## class 5:    0.0105   0.1894    0.1093     0.6909
## 
## $H8
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0305   0.2721    0.1405     0.5569
## class 2:    0.0195   0.2464    0.1518     0.5822
## class 3:    0.0668   0.2353    0.0782     0.6197
## class 4:    0.0226   0.2457    0.1082     0.6235
## class 5:    0.0192   0.2282    0.1227     0.6300
## 
## $H9
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0092   0.2454    0.1016     0.6438
## class 2:    0.0082   0.2149    0.1031     0.6738
## class 3:    0.0670   0.2371    0.0725     0.6234
## class 4:    0.0092   0.2322    0.1207     0.6379
## class 5:    0.0134   0.1957    0.0949     0.6960
## 
## $H10
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0248   0.2269    0.1073     0.6410
## class 2:    0.0160   0.2604    0.1194     0.6043
## class 3:    0.0735   0.2676    0.0630     0.5959
## class 4:    0.0123   0.2527    0.1218     0.6132
## class 5:    0.0069   0.2399    0.1155     0.6377
## 
## $H11
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0215   0.1406    0.0896     0.7483
## class 2:    0.0113   0.2225    0.1042     0.6619
## class 3:    0.0683   0.2132    0.0787     0.6397
## class 4:    0.0167   0.1906    0.0878     0.7049
## class 5:    0.0106   0.1515    0.0730     0.7649
## 
## $H12
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0608   0.5624    0.0904     0.2864
## class 2:    0.0005   0.0084    0.0287     0.9624
## class 3:    0.0607   0.2361    0.0814     0.6218
## class 4:    0.0464   0.3944    0.0740     0.4852
## class 5:    0.0462   0.4569    0.0951     0.4017
## 
## $H13
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0104   0.1541    0.0683     0.7673
## class 2:    0.0796   0.8172    0.1031     0.0000
## class 3:    0.0972   0.2881    0.0425     0.5723
## class 4:    0.0390   0.3254    0.0803     0.5552
## class 5:    0.0121   0.1281    0.0643     0.7955
## 
## $H14
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0145   0.2177    0.0809     0.6869
## class 2:    0.0000   0.0540    0.0514     0.8946
## class 3:    0.1019   0.2256    0.0739     0.5987
## class 4:    0.0175   0.2410    0.0546     0.6868
## class 5:    0.0142   0.2439    0.0740     0.6679
## 
## $H15
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0289   0.2203    0.1158     0.6350
## class 2:    0.0144   0.2149    0.1086     0.6620
## class 3:    0.1167   0.1784    0.0718     0.6331
## class 4:    0.0198   0.2140    0.0985     0.6677
## class 5:    0.0139   0.2222    0.0905     0.6734
## 
## $H16
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0082   0.0819    0.0383     0.8716
## class 2:    0.0186   0.1788    0.0912     0.7114
## class 3:    0.1176   0.2152    0.0751     0.5921
## class 4:    0.0363   0.2831    0.1023     0.5783
## class 5:    0.0230   0.2421    0.0834     0.6515
## 
## $H17
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.1339   0.7843    0.0817     0.0000
## class 2:    0.0322   0.2292    0.0561     0.6825
## class 3:    0.1027   0.2291    0.0446     0.6236
## class 4:    0.0218   0.1116    0.0435     0.8232
## class 5:    0.0017   0.0296    0.0361     0.9325
## 
## $H18
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0086   0.1119    0.0438     0.8357
## class 2:    0.0789   0.3792    0.0485     0.4934
## class 3:    0.1771   0.2042    0.0355     0.5832
## class 4:    0.0202   0.0908    0.0353     0.8536
## class 5:    0.0703   0.5727    0.0593     0.2976
## 
## $H19
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0026   0.1315    0.0529     0.8130
## class 2:    0.0587   0.2030    0.0468     0.6914
## class 3:    0.2127   0.1991    0.0098     0.5784
## class 4:    0.1536   0.7661    0.0803     0.0000
## class 5:    0.0186   0.0714    0.0522     0.8577
## 
## $H20
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0452   0.2997    0.1045     0.5506
## class 2:    0.0576   0.2598    0.0717     0.6109
## class 3:    0.3185   0.2476    0.0267     0.4073
## class 4:    0.0427   0.1693    0.0443     0.7437
## class 5:    0.0351   0.2518    0.0717     0.6415
## 
## $H21
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0285   0.2386    0.0612     0.6717
## class 2:    0.0551   0.2367    0.0918     0.6164
## class 3:    0.3231   0.1423    0.0200     0.5146
## class 4:    0.0536   0.2097    0.0905     0.6461
## class 5:    0.0340   0.2498    0.0836     0.6325
## 
## $H22
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0280   0.1609    0.0426     0.7685
## class 2:    0.0295   0.1523    0.0617     0.7565
## class 3:    0.2393   0.1856    0.0266     0.5485
## class 4:    0.0322   0.1407    0.0695     0.7577
## class 5:    0.0144   0.1424    0.0542     0.7890
## 
## $H23
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0118   0.0373    0.0152     0.9357
## class 2:    0.0058   0.0431    0.0219     0.9292
## class 3:    0.1033   0.1056    0.0129     0.7782
## class 4:    0.0037   0.0429    0.0234     0.9300
## class 5:    0.0049   0.0478    0.0187     0.9286
## 
## Estimated class population shares 
##  0.1539 0.2959 0.0876 0.1891 0.2736 
##  
## Predicted class memberships (by modal posterior prob.) 
##  0.155 0.3419 0.066 0.1898 0.2472 
##  
## ========================================================= 
## Fit for 5 latent classes: 
## ========================================================= 
## number of observations: 6153 
## number of estimated parameters: 364 
## residual degrees of freedom: 5789 
## maximum log-likelihood: -98768.13 
##  
## AIC(5): 198264.3
## BIC(5): 200712
## G^2(5): 90816.64 (Likelihood ratio/deviance statistic) 
## X^2(5): 2.237912e+18 (Chi-square goodness of fit) 
## 

day 2 data (Fig.)

## Conditional item response (column) probabilities,
##  by outcome variable, for each class (row) 
##  
## $H0
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0003   0.0194    0.0041     0.9762
## class 2:    0.0425   0.0321    0.0051     0.9204
## class 3:    0.0000   0.0096    0.0081     0.9822
## 
## $H1
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0054    0.0040     0.9907
## class 2:    0.0097   0.0324    0.0021     0.9558
## class 3:    0.0000   0.0005    0.0023     0.9972
## 
## $H2
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0018    0.0034     0.9948
## class 2:    0.0179   0.0195    0.0017     0.9608
## class 3:    0.0000   0.0012    0.0013     0.9975
## 
## $H3
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0005   0.0033    0.0032     0.9931
## class 2:    0.0032   0.0231    0.0000     0.9736
## class 3:    0.0000   0.0002    0.0025     0.9973
## 
## $H4
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0035    0.0035     0.9930
## class 2:    0.0044   0.0132    0.0000     0.9823
## class 3:    0.0004   0.0037    0.0024     0.9934
## 
## $H5
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0062    0.0061     0.9877
## class 2:    0.0028   0.0127    0.0087     0.9758
## class 3:    0.0011   0.0107    0.0026     0.9856
## 
## $H6
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0147   0.0696    0.0346     0.8811
## class 2:    0.0374   0.0880    0.0128     0.8619
## class 3:    0.0120   0.0871    0.0525     0.8484
## 
## $H7
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0098   0.1984    0.1062     0.6856
## class 2:    0.0467   0.1781    0.0739     0.7014
## class 3:    0.0138   0.2201    0.1185     0.6477
## 
## $H8
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0178   0.2335    0.1183     0.6304
## class 2:    0.0474   0.2127    0.0648     0.6751
## class 3:    0.0246   0.2599    0.1360     0.5795
## 
## $H9
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0098   0.2187    0.1032     0.6683
## class 2:    0.0695   0.2737    0.0967     0.5601
## class 3:    0.0100   0.2135    0.1091     0.6673
## 
## $H10
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0191   0.2392    0.1126     0.6291
## class 2:    0.0743   0.2300    0.0740     0.6217
## class 3:    0.0121   0.2446    0.1099     0.6334
## 
## $H11
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0135   0.2206    0.0923     0.6736
## class 2:    0.0508   0.2002    0.0619     0.6872
## class 3:    0.0044   0.0981    0.0667     0.8307
## 
## $H12
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0103   0.0830    0.0326     0.8740
## class 2:    0.0643   0.2006    0.0467     0.6885
## class 3:    0.0675   0.7961    0.1364     0.0000
## 
## $H13
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0480   0.5743    0.0853     0.2925
## class 2:    0.0887   0.3473    0.0778     0.4862
## class 3:    0.0041   0.0202    0.0560     0.9196
## 
## $H14
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0175   0.1765    0.0535     0.7524
## class 2:    0.0836   0.2426    0.0583     0.6155
## class 3:    0.0143   0.1731    0.0877     0.7248
## 
## $H15
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0134   0.2193    0.0948     0.6725
## class 2:    0.0856   0.1756    0.0473     0.6915
## class 3:    0.0175   0.2161    0.1095     0.6570
## 
## $H16
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0156   0.2147    0.0773     0.6924
## class 2:    0.0732   0.1946    0.0789     0.6533
## class 3:    0.0236   0.2021    0.0831     0.6913
## 
## $H17
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0280   0.2170    0.0443     0.7107
## class 2:    0.1047   0.1517    0.0632     0.6804
## class 3:    0.0425   0.2785    0.0408     0.6382
## 
## $H18
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0430   0.3561    0.0455     0.5554
## class 2:    0.1570   0.2285    0.0317     0.5829
## class 3:    0.0523   0.3156    0.0544     0.5776
## 
## $H19
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0428   0.2845    0.0629     0.6098
## class 2:    0.2171   0.2349    0.0342     0.5138
## class 3:    0.0431   0.2400    0.0534     0.6635
## 
## $H20
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0321   0.2477    0.0677     0.6525
## class 2:    0.3129   0.2278    0.0307     0.4287
## class 3:    0.0578   0.2462    0.0846     0.6114
## 
## $H21
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0358   0.2291    0.0905     0.6446
## class 2:    0.2734   0.1500    0.0031     0.5735
## class 3:    0.0483   0.2194    0.0774     0.6548
## 
## $H22
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0214   0.1564    0.0648     0.7574
## class 2:    0.2304   0.1756    0.0297     0.5644
## class 3:    0.0247   0.1317    0.0545     0.7891
## 
## $H23
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0013   0.0484    0.0152     0.9352
## class 2:    0.0986   0.0892    0.0052     0.8070
## class 3:    0.0027   0.0349    0.0105     0.9518
## 
## Estimated class population shares 
##  0.591 0.1178 0.2913 
##  
## Predicted class memberships (by modal posterior prob.) 
##  0.5994 0.0835 0.3171 
##  
## ========================================================= 
## Fit for 3 latent classes: 
## ========================================================= 
## number of observations: 6153 
## number of estimated parameters: 218 
## residual degrees of freedom: 5935 
## maximum log-likelihood: -98019.53 
##  
## AIC(3): 196475.1
## BIC(3): 197941.1
## G^2(3): 89400.39 (Likelihood ratio/deviance statistic) 
## X^2(3): 6.215951e+17 (Chi-square goodness of fit) 
## 

Model comparison and selection

Model Comparison. (Day 2, n = 6153)
N of classes N of parameters G^2 df AIC BIC log-likelihood
1 72 92165.61 6081 198948.3 199432.5 -99402.14
2 145 90364.49 6008 197293.2 198268.2 -98501.58
3 218 89311.03 5935 196385.7 197851.7 -97974.85
4 291 88500.33 5862 195721.0 197677.9 -97569.50
5 364 87947.21 5789 195313.9 197761.7 -97292.94
6 437 87351.06 5716 194863.7 197802.4 -96994.87
7 510 86823.89 5643 194482.6 197912.2 -96731.28
8 583 86305.78 5570 194110.5 198031.0 -96472.23
Note:
Abbreviation: N, number; G^2, the likelihood ratio statistic; df, degree of freedom; AIC, Akaike information criterion; BIC, Bayesian information criterion.

Four classes visualisation

## Conditional item response (column) probabilities,
##  by outcome variable, for each class (row) 
##  
## $H0
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0007   0.0214    0.0020     0.9760
## class 2:    0.0000   0.0092    0.0033     0.9874
## class 3:    0.0007   0.0186    0.0023     0.9784
## class 4:    0.0576   0.0327    0.0049     0.9048
## class 5:    0.0022   0.0154    0.0306     0.9517
## 
## $H1
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0093    0.0041     0.9866
## class 2:    0.0000   0.0000    0.0000     1.0000
## class 3:    0.0000   0.0030    0.0003     0.9967
## class 4:    0.0143   0.0367    0.0033     0.9458
## class 5:    0.0000   0.0032    0.0154     0.9814
## 
## $H2
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0025    0.0008     0.9968
## class 2:    0.0000   0.0000    0.0009     0.9991
## class 3:    0.0000   0.0000    0.0036     0.9964
## class 4:    0.0246   0.0211    0.0031     0.9511
## class 5:    0.0016   0.0124    0.0109     0.9751
## 
## $H3
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0066    0.0050     0.9884
## class 2:    0.0000   0.0002    0.0016     0.9982
## class 3:    0.0000   0.0000    0.0000     1.0000
## class 4:    0.0043   0.0270    0.0000     0.9688
## class 5:    0.0033   0.0021    0.0048     0.9898
## 
## $H4
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0051    0.0022     0.9927
## class 2:    0.0000   0.0033    0.0021     0.9946
## class 3:    0.0000   0.0022    0.0008     0.9970
## class 4:    0.0063   0.0154    0.0000     0.9782
## class 5:    0.0015   0.0041    0.0134     0.9809
## 
## $H5
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0000   0.0084    0.0060     0.9856
## class 2:    0.0013   0.0123    0.0000     0.9864
## class 3:    0.0000   0.0037    0.0024     0.9939
## class 4:    0.0041   0.0133    0.0067     0.9759
## class 5:    0.0000   0.0038    0.0231     0.9731
## 
## $H6
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0150   0.0840    0.0257     0.8753
## class 2:    0.0128   0.0945    0.0427     0.8499
## class 3:    0.0140   0.0688    0.0309     0.8863
## class 4:    0.0389   0.0899    0.0154     0.8557
## class 5:    0.0197   0.0123    0.0979     0.8700
## 
## $H7
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0118   0.2160    0.0823     0.6899
## class 2:    0.0159   0.2380    0.1051     0.6410
## class 3:    0.0139   0.2177    0.1101     0.6583
## class 4:    0.0474   0.1573    0.0815     0.7138
## class 5:    0.0028   0.0601    0.2056     0.7315
## 
## $H8
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0188   0.2334    0.1006     0.6472
## class 2:    0.0262   0.2783    0.1265     0.5691
## class 3:    0.0185   0.2809    0.1054     0.5952
## class 4:    0.0558   0.1903    0.0707     0.6832
## class 5:    0.0158   0.0962    0.2198     0.6682
## 
## $H9
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0144   0.2266    0.0853     0.6737
## class 2:    0.0125   0.2203    0.0827     0.6845
## class 3:    0.0082   0.2310    0.0757     0.6850
## class 4:    0.0790   0.2717    0.1049     0.5444
## class 5:    0.0063   0.1642    0.2956     0.5339
## 
## $H10
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0205   0.2501    0.0860     0.6435
## class 2:    0.0124   0.2616    0.0921     0.6339
## class 3:    0.0254   0.2568    0.1056     0.6122
## class 4:    0.0854   0.2215    0.0824     0.6107
## class 5:    0.0083   0.1196    0.2496     0.6225
## 
## $H11
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0159   0.2286    0.0687     0.6867
## class 2:    0.0047   0.1000    0.0439     0.8513
## class 3:    0.0124   0.2364    0.0746     0.6766
## class 4:    0.0641   0.1832    0.0684     0.6843
## class 5:    0.0066   0.1035    0.2516     0.6383
## 
## $H12
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0201   0.0954    0.0195     0.8650
## class 2:    0.0740   0.8197    0.1063     0.0000
## class 3:    0.0083   0.1141    0.0289     0.8487
## class 4:    0.0633   0.1898    0.0503     0.6966
## class 5:    0.0085   0.2592    0.2149     0.5174
## 
## $H13
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0494   0.5549    0.0722     0.3235
## class 2:    0.0044   0.0000    0.0344     0.9611
## class 3:    0.0581   0.6177    0.0753     0.2489
## class 4:    0.0953   0.3272    0.0856     0.4919
## class 5:    0.0101   0.2897    0.1918     0.5084
## 
## $H14
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0161   0.1831    0.0321     0.7687
## class 2:    0.0147   0.1754    0.0677     0.7421
## class 3:    0.0181   0.1706    0.0447     0.7667
## class 4:    0.1030   0.2301    0.0613     0.6057
## class 5:    0.0292   0.1958    0.2189     0.5562
## 
## $H15
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0155   0.2053    0.0676     0.7116
## class 2:    0.0195   0.2269    0.0939     0.6597
## class 3:    0.0205   0.2738    0.1027     0.6030
## class 4:    0.0946   0.1725    0.0520     0.6809
## class 5:    0.0067   0.0983    0.2001     0.6948
## 
## $H16
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0212   0.2397    0.0573     0.6817
## class 2:    0.0243   0.2036    0.0696     0.7026
## class 3:    0.0129   0.1842    0.0703     0.7326
## class 4:    0.0788   0.1879    0.0887     0.6446
## class 5:    0.0210   0.1830    0.1971     0.5989
## 
## $H17
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0350   0.3260    0.0427     0.5963
## class 2:    0.0448   0.2856    0.0332     0.6364
## class 3:    0.0199   0.0403    0.0245     0.9153
## class 4:    0.1247   0.1406    0.0694     0.6653
## class 5:    0.0357   0.2217    0.1172     0.6254
## 
## $H18
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0021   0.0530    0.0304     0.9146
## class 2:    0.0560   0.3117    0.0400     0.5923
## class 3:    0.1200   0.8357    0.0443     0.0000
## class 4:    0.1867   0.2050    0.0372     0.5711
## class 5:    0.0278   0.3053    0.1352     0.5318
## 
## $H19
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0648   0.4060    0.0526     0.4766
## class 2:    0.0504   0.2399    0.0397     0.6700
## class 3:    0.0284   0.1052    0.0486     0.8178
## class 4:    0.2582   0.2219    0.0324     0.4875
## class 5:    0.0118   0.2322    0.1559     0.6002
## 
## $H20
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0390   0.2564    0.0489     0.6558
## class 2:    0.0645   0.2451    0.0688     0.6216
## class 3:    0.0484   0.2253    0.0506     0.6758
## class 4:    0.3646   0.2159    0.0331     0.3864
## class 5:    0.0309   0.2726    0.2087     0.4878
## 
## $H21
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0410   0.2404    0.0749     0.6437
## class 2:    0.0524   0.2248    0.0700     0.6528
## class 3:    0.0473   0.2260    0.0840     0.6427
## class 4:    0.3328   0.1457    0.0000     0.5216
## class 5:    0.0298   0.1489    0.1444     0.6769
## 
## $H22
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0301   0.1588    0.0428     0.7684
## class 2:    0.0298   0.1305    0.0341     0.8056
## class 3:    0.0277   0.1647    0.0519     0.7558
## class 4:    0.2794   0.1614    0.0345     0.5247
## class 5:    0.0053   0.1405    0.2073     0.6469
## 
## $H23
##           Low_carb Med_carb High_carb Not_eating
## class 1:    0.0012   0.0450    0.0110     0.9428
## class 2:    0.0039   0.0317    0.0044     0.9600
## class 3:    0.0054   0.0556    0.0094     0.9296
## class 4:    0.1325   0.0944    0.0072     0.7659
## class 5:    0.0000   0.0582    0.0527     0.8891
## 
## Estimated class population shares 
##  0.35 0.251 0.2237 0.0797 0.0956 
##  
## Predicted class memberships (by modal posterior prob.) 
##  0.3411 0.2891 0.237 0.06 0.0728 
##  
## ========================================================= 
## Fit for 5 latent classes: 
## ========================================================= 
## number of observations: 6153 
## number of estimated parameters: 364 
## residual degrees of freedom: 5789 
## maximum log-likelihood: -97273.15 
##  
## AIC(5): 195274.3
## BIC(5): 197722.1
## G^2(5): 87907.63 (Likelihood ratio/deviance statistic) 
## X^2(5): 8.58199e+17 (Chi-square goodness of fit) 
##